But he still would suffer from problems that have afflicted Tillerson, chief among them a boss who has shown little regard for diplomacy and no qualms about undermining his secretary of state with tweets, current and former USA officials said.
Asked about Tillerson, White House spokeswoman Sarah Sanders said the secretary of state remained in his post. "Secretary Tillerson continues to lead the State Department and the entire cabinet is focused on completing this incredibly successful first year of President Trump's administration".
Tillerson would be replaced by CIA Director Mike Pompeo, known as a Trump loyalist and foreign policy hard-liner, within weeks under a White House plan to carry out the most significant staff shake-up so far of the Trump administration. Tom Cotton (R-AR) would then succeed Pompeo as director of the Central Intelligence Agency.
Baker and Haberman write that it is "not immediately clear whether Mr. Trump has given final approval to the plan", but that Chief of Staff John Kelly has drawn it up and widely circulated it.
That Mr Tillerson has struggled to forge a comfortable relationship with Mr Trump has always been an open secret in Washington. The secretary of state reportedly called Trump a "moron", a charge Tillerson never denied.
"Fox News Sunday" anchor Chris Wallace reacted on "Outnumbered Overtime", saying it "sure does seem like Tillerson is on the way out" given that White House statement.
Observers across the political and foreign policy spectrum tend to view Tillerson as a failure at the State Department.
Shortly after the news broke, Trump was peppered by reporters about the veracity of the story at the White House. On several occasions, the president publicly undercut his diplomatic initiatives.
Wallace questioned why the reported plan calls for Tillerson to stay until late January, adding the secretary is scheduled to make a trip to Europe next week to meet with key us allies.
When Tillerson was tapped for the job late previous year, many Trump critics expressed quiet relief that he'd picked a sober "adult" who could form a counterweight to the president's brasher, impulsive approach, especially on critical matters of war and peace.
Tillerson has at times put distance between himself and Trump's positions. Tillerson's advice to Trump to stay in the Paris climate deal and certify Iran's compliance with the nuclear deal was similarly overruled.
At a private dinner of foreign policy veterans last month, a senior White House official criticized Tillerson for failing to support the president's agenda, according to a person familiar with the matter.
Tillerson has taken a more hawkish view than Trump on Russian Federation and tried to mediate a dispute after four Arab nations launched a boycott of Qatar.
His tenure has coincided with the departure of dozens of veteran foreign policy hands, and numerous State Department's senior policymaking positions remain unfilled.